Potential Difference: Equation & Unit - Electricity - StudySmarter

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Potential Difference

Potential Difference

Have you ever thought about why you can hold a small battery between your fingers and feel nothing, but if you're struck by lightning you'd be lucky to survive? The answer, among other factors, is the voltage (or potential difference) of these two different sources of electricity. A typical battery may have a potential difference of 1.5 Volts, while a lightning strike can be as much as 150 million volts! This article explains what potential difference actually is, which will help you better understand why circuits behave the way they do, and why not to get struck by lightning!

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Fact Checked Content
Last Updated: 20.08.2022
Published at: 11.07.2022
11 min reading time

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Contents

Astrophysics
Atoms and Radioactivity
Circular Motion and Gravitation
Classical Mechanics
Conservation of Energy and Momentum
Dynamics
Electric Charge Field and Potential
Electricity

Ammeter
Attraction and Repulsion
Band Theory
Basics of Electricity
Batteries
Branch Analysis
Bridge Circuit
Cable Capacitance
Capacitors in Series and Parallel
Characteristic Impedance of a Cable
Circuit Schematic
Circuit Symbols
Circuits
Coaxial Cable
Complex Impedance
Conductance
Current Density
Current-Voltage Characteristics
DC Circuit
Delta Y
Dependent Sources
Drift Velocity
Drude Model
Effective Resistance
Electric Cables
Electric Cells
Electric Current
Electric Generators
Electric Motor
Electrical Power
Electrical Resistance
Electricity Generation
Electronics
Electronics and Electrical Systems
Emf and Internal Resistance
Fiber Optic Cable
Free Electron Model
Joule Heating
Kelvin Bridge
Kirchhoff's Junction Rule
Kirchhoff's Laws
Kirchhoffs Loop Rule
National Grid Physics
Network Theorems
Nodal Analysis
Non Ohmic Conductor
Norton Theorem
Ohm's Law
Ohmic Conductor
Potential Difference
Potentiometers
Power Rating
Power Transmission
RC Circuit
Reciprocity Theorem
Resistance
Resistance and Resistivity
Resistivity
Resistors
Resistors in Parallel
Resistors in Series
Resistors in Series and Parallel
Series and Parallel Circuits
Shielded Cable
Simple Circuit
Static Electricity
Superconductivity
Superposition Theorem
Theoretical Capacity
Theoretical Energy
Thevenin Theorem
Time Constant of RC Circuit
Transformer
Voltage Divider
Voltmeter
Wheatstone Bridge

Electricity and Magnetism
Electromagnetism
Electrostatics
Energy Physics
Engineering Physics
Famous Physicists
Fields in Physics
Fluids
Force
Fundamentals of Physics
Further Mechanics and Thermal Physics
Geometrical and Physical Optics
Kinematics Physics
Linear Momentum
Magnetism
Magnetism and Electromagnetic Induction
Measurements
Mechanics and Materials
Medical Physics
Modern Physics
Nuclear Physics
Oscillations
Particle Model of Matter
Physical Quantities And Units
Physics of Motion
Quantum Physics
Radiation
Rotational Dynamics
Scientific Method Physics
Solid State Physics
Space Physics
Thermodynamics
Torque and Rotational Motion
Translational Dynamics
Turning Points in Physics
Wave Optics
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Work Energy and Power

Contents

Fact Checked Content
Last Updated: 20.08.2022
11 min reading time

Content creation process designed by Lily Hulatt
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Potential Difference Definition

Potential difference (also referred to as voltage) can be a confusing concept that many students have difficulty grasping at first. But don't let that dissuade you - we can use a hydraulic analogy to more easily understand what potential difference is, and how it affects the behaviour of an electrical circuit.

Let's consider a system of pumps and reservoirs like the one shown in the diagram below. When a pump raises water to an elevated reservoir, it adds energy to the system by raising the gravitational potential energy of the water (1). The gravity acting on the elevated water means the water at the bottom of the reservoir is at high pressure (2). If we open a valve allowing the water to descend through a pipe and drive a turbine, it flows at a rate dependent on the pressure of the water and the resistance of the turbine (3). Finally, by driving the turbine, the gravitational potential energy stored in the water is converted into kinetic energy, which is removed from the system (4). The water at the bottom of the pipe has no more stored energy - until we can use a pump to add potential energy back into the water and return it to the top of the system (1).

Potential Difference Hydraulic analogy of an electrical circuit StudySmarter Diagram showing the hydraulic analogy of an electrical circuit. [Left] - a system of pumps and reservoirs which stores energy as gravitational potential and releases it as kinetic energy. [Right] - an electrical circuit that stores energy as potential difference in charge carriers, which is released as work when they pass through a resistor. StudySmarter Originals.

This system is a useful analogy of a simple electrical circuit consisting of a battery and resistor, like that shown in the diagram. The battery provides a potential difference to the charge carriers (1), which is analogous to the gravitational potential energy added to each particle of water. After passing through the battery, each electron is carrying electrical energy due to the potential difference provided by the battery (2). The charge carriers flow around the circuit which can be measured by the current $I$ dependent on the potential difference $V$ and the resistance of the circuit $R$ (3), as defined by Ohm's law:

$$V=IR$$

or in words,

Potential difference = current × resistance$$\mathrm{Potential}\;\mathrm{difference}\;=\;\mathrm{current}\;\times\;\mathrm{resistance}$$

As the charge carriers pass through the resistor their electrical energy is converted into work, using up their stored energy (4). As the charge carriers are no longer storing electrical energy, their potential difference is now zero as they flow back to the battery. When they pass through the battery again, they gain potential difference and the process repeats (1).

Hopefully this analogy helps you understand that potential difference is a measure of the amount of potential electrical energy a charge carrier holds between two points in a circuit. Potential difference is measured in the SI unit of volts $\mathrm{V}$.

The potential difference between two points in a circuit is equal to the difference in the amount of potential energy that charge carriers have per unit of charge between those two points. In other words, the energy transferred (in Joules) by charge carriers per coulomb of charge between two points in a circuit is equal to the potential difference (or voltage) between the points.

The hydraulic analogy can also be used to help understand how current, voltage, and resistance behave in series and parallel circuits.

You will be familiar with the Joule $\mathrm{J}$ as the primary unit of energy we use in physics. However, a different unit often used in nuclear and atomic physics is the electron-volt $\mathrm{eV}$!This is the quantity of energy a single electron gains when it moves through a potential difference of $1\;\mathrm{V}$. $1\;\mathrm{eV}$ is equivalent to $1.602\times10^{-19}\;\mathrm{J}$.

Potential Difference Formula

As we just established, potential difference is a measure of the difference in potential energy each unit of charge contains between two points in an electrical circuit. This means that if we know a quantity of energy transferred $E$Ebetween two points in a circuit and the amount of charge $Q$ that flowed to transfer the energy, we can calculate the potential difference $V$ between the points using the formula below:

$$V=\frac EQ\;$$

or in words,

$$\mathrm{Potential}\;\mathrm{difference}\;=\;\frac{\mathrm{energy}\;\mathrm{transferred}}{\mathrm{charge}\;\mathrm{flow}}$$

Quantity	Symbol	SI unit
Potential difference	V	V (Volts)
Energy transferred	E	J (Joule)
Charge	Q	C (Coulomb)

Potential difference unit

By studying the formula $V=\frac EQ$, we can see that a potential difference of $1\;\mathrm{V}$ is equal to $1\;\mathrm{J}$ of energy per $1\;\mathrm{C}$ of charge.

The SI unit of potential difference is the Volt $\mathrm{V}$, equivalent to one Joule-per-coulomb $(\mathrm{J}/\mathrm{C})$.

(J/C).

Potential difference equation and symbol

Another set of equations which deal with potential difference are those defined in Ohm's law, which describe how the current $I$ passing through an Ohmic electrical component is determined by the potential difference $V$ across the component and the component's electrical resistance $R$. We referred to this law and its formula earlier in the article.

Linking potential difference to electrical power

Recalling that current is the rate at which charge flows in a circuit, measured in coulombs-per-second, we can derive an equation for the power (energy-per-second) of an electrical circuit.

If we know that a certain quantity of energy $Q$ was transferred between two points in a circuit by a certain amount of charge $C$, we can calculate the potential difference $V$ of the charge between these points:

$$V=\frac EQ$$

If we also know that the energy transfer took a duration of $t$ seconds, then we can determine the current $I$:

I=Qt$$I=\frac Qt$$

Rearranging both these equations for $Q$, we get:

Q=EV,Q=It.$$\begin{array}{rcl}Q&=&\textstyle\frac EV\\Q&=&It\end{array}$$

Finally, we can combine these equations to find an equation for power $P$:

EV=ItE=IVtEt=IVP=IV$$\begin{array}{rcl}\textstyle\frac EV&=&It\\E&=&IVt\\\textstyle\frac Et&=&IV\\P&=&IV\end{array}$$

or in words,

$$\mathrm{Power}\;=\;\mathrm{current}\;\times\;\mathrm{potential}\;\mathrm{difference}$$

Potential difference in a battery

A battery adds electric potential to charge carriers as they pass through it. The battery can also be considered as the source of current in a circuit - As the positive terminal of the battery has a higher electric potential than the negative terminal, positive charges are repelled by the positive battery terminal and attracted to the negative terminal, setting up a current as they flow around the circuit. This attraction/repulsion is equivalent to gravity in the hydraulic example.

Potential difference Selection of batteries StudySmarter

Batteries in a circuit transfer stored chemical energy into charge carrying electrons, raising their potential difference as they flow through it. Flickr.

In a real electric circuit, the charge carriers are electrons - which are actually negatively charged! This means the charge carriers in a circuit move from the negative terminal to the positive terminal. When electricity was first discovered this was not yet know, and conventional current was defined as moving from positive to negative. This is the opposite of electron current, which flows from negative to positive. This difference is important to be aware of when performing circuit analysis, but it is outside the specification of the GCSE exams.

When the power source of an electric circuit transfers one Joule of energy to each coulomb of charge, we say that the power source provides one volt of potential difference.
To measure the potential difference between the two terminals of a cell, battery or an alternative power source we use a voltmeter. Voltmeters can be used to measure the potential difference across any electric circuit component or between any two points.

Potential difference Voltmeters in a circuit diagram StudySmarter Voltmeters can be used to measure the potential difference between two points in a circuit. If there is no energy being transferred between the two points the voltmeter measures between, the potential difference reading will be 0 volts. StudySmarter Originals.

Potential difference examples

Lets look at some example problems that will allow us to apply our newfound knowledge to different scenarios.

If a battery in a circuit transfers a total of $100\;\mathrm{J}$ of energy to $25\;\mathrm{C}$ of charge, what potential difference (voltage) would be measured across the terminals of the battery?

Determine what information we get from the question. We know the quantity of energy $E=100\;\mathrm{J}$. We also know that the amount of charge $Q=25\;\mathrm{C}$. The question asks us to find the potential difference, $\mathrm{V}$.
Select the correct equation to use. As the question involves the quantities $E, Q, V$, we can use $V=\frac EQ $.
Plug in values to find the answer:

$$V=\;\frac{100\;\mathrm J}{25\;\mathrm C}=4\;\mathrm J/\mathrm C=\mathbf4\boldsymbol\;\mathbf V$$

The same battery as in the previous question takes 20 seconds to transfer 240 joules of energy. What current do charge carriers/electrons flow through the battery?

Determine what information we get from the question. We already know that the potential difference of the battery isV=4 v$V=4\;\mathrm{V}$. The amount of energy transferred $E=240\;\mathrm{J}$ and the time takent=20 s$t=20\;\mathrm{s}$ .
The first step is to determine the amount of charge that flowed through the battery. We can rearrange the equationV=E/Qto $V=E/Q$ to find this: $Q=240\;\mathrm{J}/4\;\mathrm{V}=60\;\mathrm{C}$.
Now that we know the quantity of charge, we divide by the time take to find the charge-per-second, the current:

$$I=Q/t=60\;\mathrm C/20\;\mathrm s=3\;\mathrm A$$

A $1000\;\mathrm{W}$ space heater draws $4\;\mathrm{A}$ of current from its mains power supply. Determine what potential difference the appliance operates at.

Establish what information is given. The question tells us the power of the appliance $P=1000\;\mathrm{W}$, and that it draws a current of $I=4\;\mathrm{A}$. This tells us that the power is $1000\;\mathrm{joules-per-second}$ and the current is $4\;\mathrm{coulombs-per-second}$ respectively.
We can determine the potential difference from the amount of energy transferred per coulomb of charge. In one second $4\;\mathrm{C}$ transfers $1000\;\mathrm{J}$ of energy, meaning $1\;\mathrm{C}$ transfers $250\;\mathrm{J}$ .
The potential difference can be found using $V=\frac EQ$:

$$V\;=\;\frac EQ=\frac{1000\;\mathrm J}{4\;\mathrm C}=\mathbf{250}\boldsymbol\;\mathbf V$$

Potential Difference - Key takeaways

The potential difference is the amount of energy transferred per unit of charge between two points in an electric circuit.
A current will flow across a resistor if there is a potential difference or voltage across the component.
The electric potential difference between any two points can be calculated using the following formula:

$$V=\frac EQ$$

The SI unit for potential difference is the Volt $\mathrm{V}$.
The relationship between current, potential difference and resistance in an Ohmic electrical component is defined by Ohm's law:

$$V=IR$$

or in words,

$$\mathrm{Power}\;=\;\mathrm{current}\;\times\;\mathrm{potential}\;\mathrm{difference}$$

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Frequently Asked Questions about Potential Difference

What is potential difference?

The potential difference is equal to the amount of energy transferred (in joules) per unit of charge (in coulombs).

The equation for potential difference is:

V = E/Q

V is the potential difference between two points in a circuit in Volts.
Q is the amount of charge passing between the points in Coulombs.
E is the energy transferred by the charge flow in Joules.

How to calculate potential difference?

The equation for potential difference is:

V = E/Q

V is the potential difference between two points in a circuit in Volts.
Q is the amount of charge passing between the points in Coulombs.
E is the energy transferred by the charge flow in Joules.

What is the formula and examples of potential difference?

The equation for potential difference is:

V = E/Q

V is the potential difference between two points in a circuit in Volts.
Q is the amount of charge passing between the points in Coulombs.
E is the energy transferred by the charge flow in Joules.

Example: A 4V battery powers a lamp. 8J of energy is supplied to the lamp. How much charge provided this energy to the lamp?

Answer: We rearrange the formula V = E/Q to make Q the subject:

VQ = E

Q = E/V

Therefore, the charge Q is calculated by dividing the energy transferred E by the potential difference V:

Q = 8J/4V = 2C

Therefore the answer is 2 Coulombs of charge.

What is difference between electric potential and potential difference?

Electric potential at a a certain point in an electric field equals the amount of work required to bring a unit positive charge from infinity to that point.

Potential difference defines the amount of energy a charge carrier transfers (in Joules) per unit of charge between two points in a circuit. This is equal to the difference in electric potential between these two points or the work done to these charges in moving through this potential difference per unit of charge.

What is potential difference measured in?

The standard SI unit of potential difference is the Volt (V). 1 Volt is equivalent to 1 Joule of energy being transferred per Coulomb of charge.

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Tag » How To Calculate Potential Difference

Potential Difference: Equation & Unit - Electricity - StudySmarter

Potential Difference Definition

Potential Difference Formula

Potential difference unit

Potential difference equation and symbol

Linking potential difference to electrical power

Potential difference in a battery

Potential difference examples

Potential Difference - Key takeaways

Similar topics in Physics

Related topics to Electricity

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